Some modifications are presented to Sima's simple analytical model for the calculation of the total detection efficiency of a well-type gamma-ray detector (O. Sima, 2000, Nucl. Instrum. Meth. A 450, 98), aiming at improving its accuracy and broadening its applicability. The modifications pertain to some general improvements in the photon transmission probabilities through absorbing materials and implementation of specific equations for solid angle and mean path length through materials that describe the case of eccentrically positioned sources as well as volume sources.